For any hyperbolic genus one 2-bridge knot in the 3-sphere, we show that the resulting manifold by r-surgery on the knot has left-orderable fundamental group if the slope r lies in some range which depends on the knot.2010 Mathematics Subject Classification. Primary 57M25; Secondary 06F15.

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Abstract. We show that the resulting manifold by r-surgery on the knot 5 2 , which is the two-bridge knot corresponding to the rational number 3/7, has left-orderable fundamental group if the slope r satisfies 0 ≤ r ≤ 4.

We show that the resulting manifold by r-surgery on the knot 5 2 , which is the two-bridge knot corresponding to the rational number 3/7, has left-orderable fundamental group if the slope r satisfies 0 ≤ r ≤ 4.

For any hyperbolic genus-one 2-bridge knot in the 3-sphere, such as any hyperbolic twist knot, we show that the manifold resulting from r-surgery on the knot has left-orderable fundamental group if the slope r lies in some range, which depends on the knot. 57M25; 06F15